’t Hooft anomaly
E415088
’t Hooft anomaly is a quantum field theory phenomenon where a classical global symmetry cannot be consistently preserved at the quantum level, imposing powerful constraints on the dynamics and possible phases of the theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| ’t Hooft anomaly canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4142069 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: ’t Hooft anomaly Context triple: [Gerard ’t Hooft, notableWork, ’t Hooft anomaly]
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A.
Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
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B.
’t Hooft–Polyakov monopoles
’t Hooft–Polyakov monopoles are theoretical, finite-energy magnetic monopole solutions arising in certain non-abelian gauge theories with spontaneous symmetry breaking.
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C.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
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D.
Schwinger model
The Schwinger model is a two-dimensional quantum electrodynamics theory that serves as a exactly solvable toy model for studying phenomena like confinement, chiral symmetry breaking, and anomalies in quantum field theory.
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E.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: ’t Hooft anomaly Target entity description: ’t Hooft anomaly is a quantum field theory phenomenon where a classical global symmetry cannot be consistently preserved at the quantum level, imposing powerful constraints on the dynamics and possible phases of the theory.
-
A.
Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
-
B.
’t Hooft–Polyakov monopoles
’t Hooft–Polyakov monopoles are theoretical, finite-energy magnetic monopole solutions arising in certain non-abelian gauge theories with spontaneous symmetry breaking.
-
C.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
-
D.
Schwinger model
The Schwinger model is a two-dimensional quantum electrodynamics theory that serves as a exactly solvable toy model for studying phenomena like confinement, chiral symmetry breaking, and anomalies in quantum field theory.
-
E.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
anomaly in quantum field theory
ⓘ
quantum field theory concept ⓘ |
| appliesTo |
chiral symmetry
ⓘ
continuous symmetry ⓘ discrete symmetry ⓘ flavor symmetry ⓘ global symmetry ⓘ higher-form symmetry ⓘ parity symmetry ⓘ time-reversal symmetry ⓘ |
| canBeComputedBy |
Feynman diagrams
ⓘ
anomaly polynomial in higher dimensions ⓘ index theorems ⓘ |
| canBeInterpretedAs | boundary anomaly of a higher-dimensional bulk theory ⓘ |
| characterizes |
inconsistency of classical symmetry at quantum level
ⓘ
obstruction to gauging a global symmetry ⓘ |
| distinguishedFrom |
explicit symmetry breaking
ⓘ
gauge anomaly ⓘ |
| formalizedBy | ’t Hooft anomaly matching condition ⓘ |
| implies |
constraints on infrared dynamics
ⓘ
constraints on possible phases of a theory ⓘ constraints on renormalization group flows ⓘ global symmetry cannot be consistently gauged ⓘ nontrivial infrared degrees of freedom ⓘ symmetry realization cannot be trivially gapped ⓘ |
| namedAfter |
Gerard 't Hooft
ⓘ
linked to:
Gerard ’t Hooft
|
| occursIn |
conformal field theory
ⓘ
lattice gauge theories ⓘ quantum chromodynamics ⓘ supersymmetric gauge theories ⓘ |
| persistsUnder | renormalization group flow ⓘ |
| relatesTo |
Adler–Bell–Jackiw anomaly
ⓘ
Wess–Zumino–Witten term ⓘ
linked to:
Wess–Zumino–Witten model
anomaly matching ⓘ anomaly polynomial ⓘ chiral anomaly ⓘ conserved currents ⓘ gauge anomaly ⓘ global symmetry ⓘ path integral measure ⓘ quantum field theory ⓘ symmetry-protected topological phase ⓘ topological quantum field theory ⓘ ’t Hooft anomaly inflow ⓘ ’t Hooft anomaly matching condition ⓘ |
| requires | matching of anomalies between ultraviolet and infrared descriptions ⓘ |
| usedFor |
classifying symmetry-protected topological phases
ⓘ
constraining chiral symmetry breaking patterns ⓘ constraining confinement scenarios ⓘ diagnosing symmetry fractionalization ⓘ testing candidate infrared dualities ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: ’t Hooft anomaly Description of subject: ’t Hooft anomaly is a quantum field theory phenomenon where a classical global symmetry cannot be consistently preserved at the quantum level, imposing powerful constraints on the dynamics and possible phases of the theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.